On the non-existence for quantum LDPC codes of type IEEE802.16e with rates 1/2 and 2/3B

TL;DR

This paper investigates the possibility of constructing CSS quantum codes from practical irregular LDPC codes based on IEEE802.16e standards, proving such constructions are impossible for certain rates.

Contribution

It is the first to analyze the feasibility of CSS code construction using IEEE802.16e-based irregular LDPC codes, demonstrating their non-existence at specific rates.

Findings

Proved impossibility of CSS code construction with IEEE802.16e LDPC codes at rates 1/2 and 2/3B.

First analysis of practical irregular LDPC codes for quantum CSS code construction.

Highlights limitations of using IEEE802.16e codes in quantum error correction.

Abstract

In this paper, we discuss a construction of CSS codes derived from pairs of practical irregular LDPC codes. Our design of irregular LDPC codes is based the design written in the standardization of IEEE802.16e. Our research has tried to make a CSS code with a pair of LDPC codes of type IEEE802.16e. To our regret, we proved that it was impossible to construct a CSS code if one of classical codes was of type IEEE802.16e with rate 1/2 and 2/3B. We would like to report the discussion on its impossibility in this paper. This is the first paper to analyze the possibility of a CSS code construction by using two irregular LDPC codes which are practically useful.